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Stability analysis of a two-station cascade queueing network

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  • E. Morozov
  • B. Steyaert

Abstract

We consider a two-station cascade network, where the first station has Poisson input and the second station has renewal input, with i.i.d. service times at both stations. The following partial interaction exists between stations: whenever the second station becomes empty while customers are awaiting service at the first one, one customer can jump to the second station to be served there immediately. However, the first station cannot assist the second one in the opposite case. For this system, we establish necessary and sufficient stability conditions of the basic workload process, using a regenerative method. An extension of the basic model, including a multiserver first station, a different service time distribution for customers jumping from station 1 to station 2, and an arbitrary threshold d 1 ≥1 on the queue-size at station 1 allowing jumps to station 2, are also treated. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • E. Morozov & B. Steyaert, 2013. "Stability analysis of a two-station cascade queueing network," Annals of Operations Research, Springer, vol. 202(1), pages 135-160, January.
    • Handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:135-160:10.1007/s10479-011-1034-9
    DOI: 10.1007/s10479-011-1034-9
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    References listed on IDEAS

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    Cited by:

    1. Masakiyo Miyazawa & Evsey Morozov, 2023. "Stability of a cascade system with two stations and its extension for multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 155-174, August.
    2. K. Avrachenkov & E. Morozov & B. Steyaert, 2016. "Sufficient stability conditions for multi-class constant retrial rate systems," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 149-171, February.
    3. Rosario Delgado, 2016. "A two-queue polling model with priority on one queue and heavy-tailed On/Off sources: a heavy-traffic limit," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 57-85, June.
    4. Masakiyo Miyazawa & Evsey Morozov, 2022. "Stability condition of a cascade system with a general number of stations," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 225-227, April.
    5. Bara Kim & Jeongsim Kim, 2023. "Stability of a cascade system with multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 53-64, June.
    6. Hong Zhang & Saviour Worlanyo Akuamoah & Wilson Osafo Apeanti & Prince Harvim & David Yaro & Paul Georgescu, 2021. "The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector," Mathematics, MDPI, vol. 9(16), pages 1-21, August.

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